To complete the missing reasons for the proof, let's go through the steps:
Given: [tex]\(4(x-2) = 6x + 18\)[/tex]
1. [tex]\(4(x-2) = 6x + 18\)[/tex]
- Reason: Given
2. [tex]\(4x - 8 = 6x + 18\)[/tex]
- Reason: Distributive property. We distribute [tex]\(4\)[/tex] across the terms inside the parentheses.
3. [tex]\(-2x - 8 = 18\)[/tex]
- Reason: Subtraction property of equality. We subtract [tex]\(6x\)[/tex] from both sides of the equation to isolate the [tex]\(x\)[/tex] terms on one side.
4. [tex]\(-2x = 26\)[/tex]
- Reason: Addition property of equality. We add [tex]\(8\)[/tex] to both sides of the equation to isolate the [tex]\(-2x\)[/tex] term.
5. [tex]\(x = -13\)[/tex]
- Reason: Division property of equality. We divide both sides by [tex]\(-2\)[/tex] to solve for [tex]\(x\)[/tex].
So, the correct missing reasons are:
[tex]\[
\begin{array}{|l|l|}
\hline
\text{Statements} & \text{Reasons} \\
\hline
1. \quad 4(x-2) = 6x + 18 & \text{given} \\
\hline
2. \quad 4x - 8 = 6x + 18 & \text{distributive property} \\
\hline
3. \quad -2x - 8 = 18 & \text{subtraction property of equality} \\
\hline
4. \quad -2x = 26 & \text{addition property of equality} \\
\hline
5. \quad x = -13 & \text{division property of equality} \\
\hline
\end{array}
\][/tex]
Thus, the correct choices to complete the missing reasons are [tex]\(3. \text{subtraction property of equality}\)[/tex] and [tex]\(5. \text{division property of equality}\)[/tex]. The answer is:
- [tex]\(3. \text{subtraction property of equality}; 5. \text{division property of equality}\)[/tex]
